# Thread: Bionomial & Approximation Distribution - Probability

1. ## Bionomial & Approximation Distribution - Probability

What is the probability of getting exactly 40 heads if a fair coin is tossed 50 times, using:

a) The binomial distribution formula?
b) The normal approximation to the binomial distribution?

a) p(x) = c(n,x) p^x q ^n-x
p(x=40) = c(50,40) (4/5)^40 (4/5)^10

Now would that be correct??? I do that and I get a ridiculous number.

b) SD(standard deviation)= Squareroot(SR) of =npq
Sd=SR 50x0.8x0.2
SD= SR = 8
SD= 2.83

z = 39.5 - 50/2.83 = -10.5/2.83 = -3.71

Using the z-score table 0.4999 = 49.9% of getting exactly 40 heads.

Something seems off, can someone direct me to where I am going wrong?

2. ## Re: Bionomial & Approximation Distribution - Probability

$p,$ the probability of the coin coming down heads, is 1/2 not 4/5.

3. ## Re: Bionomial & Approximation Distribution - Probability

So other then that, I am on the correct track??

4. ## Re: Bionomial & Approximation Distribution - Probability

exact prob is

${50\choose 40}(.5)^{50}$

normal approximation is

$P(39.5

where

$\mu= np=50(.5)$ and $\sigma^2=npq=50(.25)$